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Sudakov-Fernique post-AMP, and a new proof of the local convexity of the TAP free energy. (arXiv:2208.09550v1 [math.PR])
Aug. 23, 2022, 1:10 a.m. | Michael Celentano
cs.LG updates on arXiv.org arxiv.org
In many problems in modern statistics and machine learning, it is often of
interest to establish that a first order method on a non-convex risk function
eventually enters a region of parameter space in which the risk is locally
convex. We derive an asymptotic comparison inequality, which we call the
Sudakov-Fernique post-AMP inequality, which, in a certain class of problems
involving a GOE matrix, is able to probe properties of an optimization
landscape locally around the iterates of an approximate …
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